diff --git a/__init__.py b/__init__.py index 8b137891..e69de29b 100644 --- a/__init__.py +++ b/__init__.py @@ -1 +0,0 @@ - diff --git a/active_projects/eop/chapter2.py b/active_projects/eop/chapter2.py new file mode 100644 index 00000000..f3cb0057 --- /dev/null +++ b/active_projects/eop/chapter2.py @@ -0,0 +1,103 @@ +from big_ol_pile_of_manim_imports import * + +def print_permutation(index_list): + + + n = max(max(index_list), len(index_list)) + for i in range(0,n): + if index_list[i] > n - i: + raise Exception("Impossible indices!") + + #print "given index list:", index_list + perm_list = n * ["_"] + alphabet = ["A", "B", "C", "D", "E", "F", + "G", "H", "I", "J", "K", "L", + "M", "N", "O", "P", "Q", "R", + "S", "T", "U", "V", "W", "X", + "Y", "Z"] + free_indices = range(n) + free_indices_p1 = range(1,n + 1) + #print perm_list + for i in range(n): + findex = index_list[i] - 1 + #print "place next letter at", findex + 1, "th free place" + tindex = free_indices[findex] + #print "so at position", tindex + 1 + perm_list[tindex] = alphabet[i] + free_indices.remove(tindex) + free_indices_p1.remove(tindex + 1) + #print "remaining free places:", free_indices_p1 + #print perm_list + + return "".join(perm_list) + + +class PermutationGrid(Scene): + + def text_box(self, str): + box = TextMobject(str).scale(0.3) + box.add(SurroundingRectangle(box, stroke_color = DARK_GREY)) + return box + + + def construct(self): + + + N = 5 + + index_list = [] + perm5_box = VGroup() + for i in range(1, N + 1): + index_list.append(i) + perm4_box = VGroup() + for j in range(1, N): + index_list.append(j) + perm3_box = VGroup() + for k in range(1, N - 1): + index_list.append(k) + perm2_box = VGroup() + for l in range(1, N - 2): + index_list.append(l) + index_list.append(1) + perm_box = self.text_box(print_permutation(index_list)) + if l > 1: + perm_box.next_to(perm2_box[-1], DOWN, buff = 0) + perm2_box.add(perm_box) + index_list.pop() + index_list.pop() + if k > 1: + perm2_box.next_to(perm3_box[-1], RIGHT, buff = 0.08) + perm3_box.add(perm2_box) + index_list.pop() + perm3_box.add(SurroundingRectangle(perm3_box, buff = 0.12, stroke_color = LIGHT_GRAY)) + if j > 1: + perm3_box.next_to(perm4_box[-1], DOWN, buff = 0) + perm4_box.add(perm3_box) + index_list.pop() + if i > 1: + perm4_box.next_to(perm5_box[-1], RIGHT, buff = 0.16) + perm5_box.add(perm4_box) + index_list.pop() + + perm5_box.move_to(ORIGIN) + self.add(perm5_box) + + + + + + + + + + + + + + + + + + + + diff --git a/active_projects/name_animation.py b/active_projects/name_animation.py index 2ff96bff..112669d7 100644 --- a/active_projects/name_animation.py +++ b/active_projects/name_animation.py @@ -1,3 +1,6 @@ +#!/usr/bin/env python2 +# -*- coding: utf-8 -*- + from big_ol_pile_of_manim_imports import * NAME_WITH_SPACES = "Prime Meridian" @@ -5,71 +8,100 @@ DIAMETER = 3.0 RADIUS = DIAMETER / 2 LETTER_SCALE = 1 + class NameAnimationScene(Scene): + CONFIG = { + "animated_name": "Prime Meridian" + } def construct(self): - - name = ''.join(NAME_WITH_SPACES.split(' ')) - letters = list(name) - nb_letters = len(letters) + name = self.animated_name + letter_mobs = TextMobject(name) + nb_letters = len(letter_mobs) randy = PiCreature() randy.move_to(ORIGIN).scale_to_fit_height(0.5 * DIAMETER) randy.set_color(BLUE_E) randy.look_at(UP + RIGHT) self.add(randy) - dtheta = TAU/nb_letters - angles = np.arange(TAU/4,-3 * TAU / 4,-dtheta) + dtheta = TAU / nb_letters + angles = np.arange(TAU / 4, -3 * TAU / 4, -dtheta) name_mob = VGroup() - for (letter, angle) in zip(letters, angles): - letter_mob = TextMobject(letter).scale(LETTER_SCALE) + for (letter_mob, angle) in zip(letter_mobs, angles): + letter_mob.scale(LETTER_SCALE) pos = RADIUS * np.cos(angle) * RIGHT + RADIUS * np.sin(angle) * UP letter_mob.move_to(pos) name_mob.add(letter_mob) - pos2 = RADIUS * np.cos(angles[2]) * RIGHT + RADIUS * np.sin(angles[2]) * UP + pos2 = RADIUS * np.cos(angles[2]) * RIGHT + \ + RADIUS * np.sin(angles[2]) * UP + + times_n_label = VGroup( + TexMobject("\\times"), + Integer(1) + ) + times_n_label.arrange_submobjects(RIGHT) + times_n_label.shift(FRAME_WIDTH * RIGHT / 4) + times_n_label.to_edge(UP) self.play( - LaggedStart(Write, name_mob, run_time = 3), - ApplyMethod(randy.look_at, pos2, run_time = 3) + LaggedStart(FadeIn, name_mob, run_time=3), + ApplyMethod(randy.change, "pondering", pos2, run_time=1), + FadeIn(times_n_label) ) - for i in range(2,nb_letters + 2): + for n in range(2, nb_letters + 2): group = [] - for (j,letter_mob) in enumerate(name_mob.submobjects): + for (j, letter_mob) in enumerate(name_mob.submobjects): - new_angle = TAU / 4 - i * j * dtheta - new_pos = RADIUS * np.cos(new_angle) * RIGHT + RADIUS * np.sin(new_angle) * UP + new_angle = TAU / 4 - n * j * dtheta + new_pos = RADIUS * np.cos(new_angle) * \ + RIGHT + RADIUS * np.sin(new_angle) * UP letter_mob.target = letter_mob.copy().move_to(new_pos) - anim = MoveToTarget(letter_mob, path_arc = - j * dtheta) + anim = MoveToTarget(letter_mob, path_arc=- j * dtheta) group.append(anim) - + new_n = Integer(n) + new_n.move_to(times_n_label[1]) self.play( - AnimationGroup(*group, run_time = 3), - ApplyMethod(randy.look_at,name_mob.submobjects[2], run_time = 3) + AnimationGroup(*group, run_time=3), + UpdateFromFunc(randy, lambda r: r.look_at(name_mob.submobjects[2])), + FadeOut(times_n_label[1]), + FadeIn(new_n) ) + times_n_label.submobjects[1] = new_n self.wait(0.5) - thank_you = TextMobject("Thank You!").next_to(randy, DOWN) new_randy = randy.copy() new_randy.change("hooray") new_randy.set_color(BLUE_E) new_randy.look_at(ORIGIN) self.play( - Transform(name_mob, thank_you), + ReplacementTransform(name_mob, VGroup(*thank_you)), Transform(randy, new_randy) ) + self.play(Blink(randy)) + + def __str__(self): + return self.animated_name.replace(" ", "") + "Animation" +names = [] - - - - - - - - - +if __name__ == "__main__": + for name in names: + try: + NameAnimationScene( + frame_duration=PRODUCTION_QUALITY_FRAME_DURATION, + camera_config=PRODUCTION_QUALITY_CAMERA_CONFIG, + animated_name=name, + write_to_movie=True, + output_directory=os.path.join( + ANIMATIONS_DIR, + "active_projects", + "name_animations", + ), + ) + except Exception as e: + print "Could not animate %s: %s" % (name, e) diff --git a/active_projects/wallis_g.py b/active_projects/wallis_g.py index 64a67fbf..493aa117 100644 --- a/active_projects/wallis_g.py +++ b/active_projects/wallis_g.py @@ -25,15 +25,387 @@ def get_chord_f_label(chord, arg="f", direction=DOWN): chord_f.angle = angle return chord_f + +class WallisNumeratorDenominatorGenerator(object): + def __init__(self): + self.n = 0 + + def __iter__(self): + return self + + def __next__(self): + return self.next() + + def next(self): + n = self.n + self.n += 1 + if n % 2 == 0: + return (n + 2, n + 1) + else: + return (n + 1, n + 2) + + +def get_wallis_product(n_terms=6, show_result=True): + tex_mob_args = [] + nd_generator = WallisNumeratorDenominatorGenerator() + for x in range(n_terms): + numerator, denominator = nd_generator.next() + tex_mob_args += [ + "{%d" % numerator, "\\over", "%d}" % denominator, "\\cdot" + ] + tex_mob_args[-1] = "\\cdots" + if show_result: + tex_mob_args += ["=", "{\\pi", "\\over", "2}"] + + result = TexMobject(*tex_mob_args) + return result + + +def get_wallis_product_numerical_terms(n_terms=20): + result = [] + nd_generator = WallisNumeratorDenominatorGenerator() + for x in range(n_terms): + n, d = nd_generator.next() + result.append(float(n) / d) + return result + + # Scenes +class Introduction(Scene): + def construct(self): + n_terms = 10 + + number_line = NumberLine( + x_min=0, + x_max=2, + unit_size=5, + tick_frequency=0.25, + numbers_with_elongated_ticks=[0, 1, 2], + color=LIGHT_GREY, + ) + number_line.add_numbers() + number_line.move_to(DOWN) + + numerical_terms = get_wallis_product_numerical_terms(400) + partial_products = np.cumprod(numerical_terms) + curr_product = partial_products[0] + + arrow = Vector(DOWN, color=YELLOW) + + def get_arrow_update(): + return ApplyFunction( + lambda mob: mob.next_to( + number_line.number_to_point(curr_product), + UP, SMALL_BUFF + ), + arrow, + ) + get_arrow_update().update(1) + decimal = DecimalNumber(curr_product, num_decimal_points=5, show_ellipsis=True) + decimal.next_to(arrow, UP, SMALL_BUFF, submobject_to_align=decimal[:5]) + decimal_anim = ChangingDecimal( + decimal, + lambda a: number_line.point_to_number(arrow.get_center()), + tracked_mobject=arrow + ) + + product_mob = get_wallis_product(n_terms) + product_mob.to_edge(UP) + + rects = VGroup(*[ + SurroundingRectangle(product_mob[:n]) + for n in range(3, 4 * n_terms, 4) + [4 * n_terms] + ]) + rect = rects[0].copy() + + pi_halves_arrow = Vector(UP, color=BLUE) + pi_halves_arrow.next_to( + number_line.number_to_point(np.pi / 2), DOWN, SMALL_BUFF + ) + pi_halves_term = TexMobject("\\pi / 2") + pi_halves_term.next_to(pi_halves_arrow, DOWN) + + self.add(product_mob, number_line, rect, arrow, decimal) + self.add(pi_halves_arrow, pi_halves_term) + for n in range(1, len(rects)): + curr_product = partial_products[n] + self.play( + get_arrow_update(), + decimal_anim, + Transform(rect, rects[n]), + run_time=0.5 + ) + self.wait(0.5) + + for n in range(len(rects), len(numerical_terms), 31): + curr_product = partial_products[n] + self.play( + get_arrow_update(), + decimal_anim, + run_time=0.25 + ) + curr_product = np.pi / 2 + self.play( + get_arrow_update(), + decimal_anim, + run_time=0.5 + ) + self.wait() + + +class SourcesOfOriginality(TeacherStudentsScene): + def construct(self): + self.mention_excitement() + self.break_down_value_of_math_presentations() + self.where_we_fit_in() + + def mention_excitement(self): + self.teacher_says( + "This one came about \\\\ a bit differently...", + target_mode="speaking", + run_time=1 + ) + self.change_student_modes("happy", "confused", "erm") + self.wait(2) + + def break_down_value_of_math_presentations(self): + title = TextMobject("The value of a", "math", "presentation") + title.to_edge(UP, buff=MED_SMALL_BUFF) + value_of, math, presentation = title + + MATH_COLOR = YELLOW + COMMUNICATION_COLOR = BLUE + + big_rect = self.big_rect = Rectangle( + width=title.get_width() + 2 * MED_LARGE_BUFF, + height=3.5, + color=WHITE + ) + big_rect.next_to(title, DOWN) + + left_rect, right_rect = self.left_rect, self.right_rect = [ + Rectangle( + height=big_rect.get_height() - 2 * SMALL_BUFF, + width=0.5 * big_rect.get_width() - 2 * SMALL_BUFF, + color=color + ) + for color in MATH_COLOR, COMMUNICATION_COLOR + ] + right_rect.flip() + left_rect.next_to(big_rect.get_left(), RIGHT, SMALL_BUFF) + right_rect.next_to(big_rect.get_right(), LEFT, SMALL_BUFF) + + underlying_math = TextMobject("Underlying", "math") + underlying_math.set_color(MATH_COLOR) + communication = TextMobject("Communication") + communication.set_color(COMMUNICATION_COLOR) + VGroup(underlying_math, communication).scale(0.75) + underlying_math.next_to(left_rect.get_top(), DOWN, SMALL_BUFF) + communication.next_to(right_rect.get_top(), DOWN, SMALL_BUFF) + + formula = TexMobject( + "\\sum_{n = 1}^\\infty \\frac{1}{n^2} = \\frac{\\pi^2}{2}", + ) + formula.scale(0.75) + formula.next_to(underlying_math, DOWN) + + based_on_wastlund = TextMobject( + "Previous video based on\\\\", + "a paper by Johan W\\\"{a}stlund" + ) + based_on_wastlund.scale_to_fit_width(left_rect.get_width() - MED_SMALL_BUFF) + based_on_wastlund.next_to(formula, DOWN, MED_LARGE_BUFF) + + communication_parts = TextMobject("Visuals, narrative, etc.") + communication_parts.scale(0.75) + communication_parts.next_to(communication, DOWN, MED_LARGE_BUFF) + lighthouse = Lighthouse(height=0.5) + lighthouse.next_to(communication_parts, DOWN, LARGE_BUFF) + ambient_light = AmbientLight( + num_levels=200, + radius=5, + opacity_function=DEFAULT_OPACITY_FUNCTION, + ) + ambient_light.move_source_to(lighthouse.get_top()) + + big_rect.save_state() + big_rect.stretch(0, 1) + big_rect.stretch(0.5, 0) + big_rect.move_to(title) + + self.play( + FadeInFromDown(title), + RemovePiCreatureBubble( + self.teacher, + target_mode="raise_right_hand", + look_at_arg=title, + ), + self.get_student_changes( + *["pondering"] * 3, + look_at_arg=title + ) + ) + self.play(big_rect.restore) + self.play(*map(ShowCreation, [left_rect, right_rect])) + self.wait() + self.play( + math.match_color, left_rect, + ReplacementTransform(VGroup(math.copy()), underlying_math) + ) + self.play(FadeIn(formula)) + self.play( + presentation.match_color, right_rect, + ReplacementTransform(presentation.copy(), communication) + ) + self.play( + FadeIn(communication_parts), + FadeIn(lighthouse), + SwitchOn(ambient_light) + ) + self.play(self.teacher.change, "tease") + self.wait() + + self.play( + FadeIn(based_on_wastlund), + self.get_student_changes( + "sassy", "erm", "plain", + look_at_arg=based_on_wastlund + ), + ) + self.wait() + + self.math_content = VGroup(formula, based_on_wastlund) + + def where_we_fit_in(self): + right_rect = self.right_rect + left_rect = self.left_rect + + points = [ + right_rect.get_left() + SMALL_BUFF * RIGHT, + right_rect.get_corner(UL), + right_rect.get_corner(UR), + right_rect.get_right() + SMALL_BUFF * LEFT, + right_rect.get_corner(DR), + right_rect.get_bottom() + SMALL_BUFF * UP, + right_rect.get_corner(DL), + ] + added_points = [ + left_rect.get_bottom(), + left_rect.get_corner(DL), + left_rect.get_corner(DL) + 1.25 * UP, + left_rect.get_bottom() + 1.25 * UP, + ] + + blob1, blob2 = VMobject(), VMobject() + blob1.set_points_smoothly(points + [points[0]]) + blob1.add_control_points(3 * len(added_points) * [points[0]]) + blob2.set_points_smoothly(points + added_points + [points[0]]) + for blob in blob1, blob2: + blob.set_stroke(width=0) + blob.set_fill(BLUE, opacity=0.5) + + our_contribution = TextMobject("Our target \\\\ contribution") + our_contribution.scale(0.75) + our_contribution.to_corner(UR) + arrow = Arrow( + our_contribution.get_bottom(), + right_rect.get_right() + MED_LARGE_BUFF * LEFT, + color=BLUE + ) + + wallis_product = get_wallis_product(n_terms=4) + wallis_product.scale_to_fit_width(left_rect.get_width() - 2 * MED_LARGE_BUFF) + wallis_product.move_to(self.math_content, UP) + wallis_product_name = TextMobject("``Wallis product''") + wallis_product_name.scale(0.75) + wallis_product_name.next_to(wallis_product, DOWN, MED_SMALL_BUFF) + + new_proof = TextMobject("New proof") + new_proof.next_to(wallis_product_name, DOWN, MED_LARGE_BUFF) + + self.play( + DrawBorderThenFill(blob1), + Write(our_contribution), + GrowArrow(arrow), + ) + self.wait(2) + self.play(FadeOut(self.math_content)) + self.play( + FadeIn(wallis_product), + Write(wallis_product_name, run_time=1) + ) + self.wait(2) + self.play( + Transform(blob1, blob2, path_arc=-90 * DEGREES), + FadeIn(new_proof), + self.teacher.change, "hooray", + ) + self.change_all_student_modes("hooray", look_at_arg=new_proof) + self.wait(5) + + +class SridharWatchingScene(PiCreatureScene): + CONFIG = { + "default_pi_creature_kwargs": { + "color": YELLOW_E, + "flip_at_start": False, + }, + } + + def construct(self): + laptop = Laptop() + laptop.scale(1.8) + laptop.to_corner(DR) + sridhar = self.pi_creature + sridhar.next_to(laptop, LEFT, SMALL_BUFF, DOWN) + bubble = ThoughtBubble() + bubble.flip() + bubble.pin_to(sridhar) + + basel = TexMobject( + "{1", "\\over", "1^2}", "+" + "{1", "\\over", "2^2}", "+" + "{1", "\\over", "3^2}", "+", "\\cdots", + "= \\frac{\\pi^2}{6}" + ) + wallis = get_wallis_product(n_terms=4) + VGroup(basel, wallis).scale(0.7) + basel.move_to(bubble.get_bubble_center()) + basel.to_edge(UP, buff=MED_SMALL_BUFF) + wallis.next_to(basel, DOWN, buff=0.75) + arrow = TexMobject("\\updownarrow") + arrow.move_to(VGroup(basel, wallis)) + basel.set_color(YELLOW) + wallis.set_color(BLUE) + + self.play(LaggedStart(DrawBorderThenFill, laptop)) + self.play(sridhar.change, "pondering", laptop.screen) + self.wait() + self.play(ShowCreation(bubble)) + self.play(LaggedStart(FadeIn, basel)) + self.play( + ReplacementTransform(basel.copy(), wallis), + GrowFromPoint(arrow, arrow.get_top()) + ) + self.wait(4) + self.play(sridhar.change, "thinking", wallis) + self.wait(4) + self.play(LaggedStart( + ApplyFunction, + VGroup(*list(laptop) + [bubble, basel, arrow, wallis, sridhar]), + lambda mob: (lambda m: m.set_color(BLACK).fade(1).scale(0.8), mob), + run_time=3, + )) + + class DistanceProductScene(MovingCameraScene): CONFIG = { "ambient_light_config": { "opacity_function": DEFAULT_OPACITY_FUNCTION, "num_levels": 100, - "light_radius": 5, + "radius": 5, "max_opacity": 0.8, "color": PRODUCT_COLOR, }, @@ -53,6 +425,7 @@ class DistanceProductScene(MovingCameraScene): "numeric_distance_label_height": 0.25, "default_product_column_top": FRAME_WIDTH * RIGHT / 4 + 1.5 * UP, "include_lighthouses": True, + "include_distance_labels_background_rectangle": True, } def setup(self): @@ -112,11 +485,15 @@ class DistanceProductScene(MovingCameraScene): self.lights.add(light) return self.lights - def get_distance_lines(self): - self.distance_lines = VGroup(*[ - Line(self.get_observer_point(), point) + def get_distance_lines(self, start_point=None, line_class=Line): + if start_point is None: + start_point = self.get_observer_point() + lines = VGroup(*[ + line_class(start_point, point) for point in self.get_lh_points() ]) + lines.set_stroke(width=2) + self.distance_lines = lines return self.distance_lines def get_symbolic_distance_labels(self): @@ -132,20 +509,22 @@ class DistanceProductScene(MovingCameraScene): self.d_labels.add(d_label) return self.d_labels - def get_numeric_distance_labels(self, num_decimal_points=3, show_ellipsis=True): + def get_numeric_distance_labels(self, lines=None, num_decimal_points=3, show_ellipsis=True): radius = self.circle.get_width() / 2 - if not hasattr(self, "distance_lines"): - self.get_distance_lines() + if lines is None: + if not hasattr(self, "distance_lines"): + self.get_distance_lines() + lines = self.distance_lines labels = self.numeric_distance_labels = VGroup() - for line in self.distance_lines: + for line in lines: label = DecimalNumber( line.get_length() / radius, num_decimal_points=num_decimal_points, show_ellipsis=show_ellipsis, - include_background_rectangle=True, + include_background_rectangle=self.include_distance_labels_background_rectangle, ) label.scale_to_fit_height(self.numeric_distance_label_height) - max_width = 0.5 * line.get_length() + max_width = 0.5 * max(line.get_length(), 0.1) if label.get_width() > max_width: label.scale_to_fit_width(max_width) angle = (line.get_angle() % TAU) - TAU / 2 @@ -157,12 +536,13 @@ class DistanceProductScene(MovingCameraScene): labels.add(label) return labels - def get_distance_product_column(self, column_top): - if not hasattr(self, "numeric_distance_labels"): - self.get_numeric_distance_labels() + def get_distance_product_column(self, column_top, labels=None, fraction=None): if column_top is None: column_top = self.default_product_column_top - labels = self.numeric_distance_labels + if labels is None: + if not hasattr(self, "numeric_distance_labels"): + self.get_numeric_distance_labels() + labels = self.numeric_distance_labels stacked_labels = labels.copy() for label in stacked_labels: label.rotate(-label.angle) @@ -177,17 +557,35 @@ class DistanceProductScene(MovingCameraScene): times.next_to(h_line, UP, SMALL_BUFF, aligned_edge=LEFT) product_decimal = DecimalNumber( - self.get_distance_product(), + self.get_distance_product(fraction), num_decimal_points=3, show_ellipsis=True, - include_background_rectangle=True, + include_background_rectangle=self.include_distance_labels_background_rectangle, ) product_decimal.scale_to_fit_height(self.numeric_distance_label_height) product_decimal.next_to(h_line, DOWN) product_decimal.align_to(stacked_labels, RIGHT) - product_decimal.set_color(BLUE) + product_decimal[1].set_color(BLUE) return VGroup(stacked_labels, h_line, times, product_decimal) + def get_fractional_arc(self, fraction, start_fraction=0): + arc = Arc( + angle=fraction * TAU, + start_angle=start_fraction * TAU, + radius=self.get_radius(), + ) + arc.shift(self.circle.get_center()) + return arc + + def get_halfway_indication_arcs(self): + fraction = 0.5 / self.num_lighthouses + arcs = VGroup( + self.get_fractional_arc(fraction), + self.get_fractional_arc(-fraction, start_fraction=2 * fraction), + ) + arcs.set_stroke(YELLOW, 4) + return arcs + def get_circle_group(self): group = VGroup(self.circle) if not hasattr(self, "observer_dot"): @@ -254,17 +652,14 @@ class DistanceProductScene(MovingCameraScene): class IntroduceDistanceProduct(DistanceProductScene): CONFIG = { - "ambient_light_config": { - # "num_levels": 10, - # "radius": 1, - "color": YELLOW, - }, + "ambient_light_config": {"color": YELLOW}, } def construct(self): self.draw_circle_with_points() self.turn_into_lighthouses_and_observer() self.show_sum_of_inverse_squares() + self.transition_to_lemma_1() def draw_circle_with_points(self): circle = self.circle @@ -483,15 +878,44 @@ class IntroduceDistanceProduct(DistanceProductScene): )) self.wait() + def transition_to_lemma_1(self): + self.lighthouse_height = Lemma1.CONFIG["lighthouse_height"] + self.circle_radius = Lemma1.CONFIG["circle_radius"] + self.observer_fraction = Lemma1.CONFIG["observer_fraction"] + + self.ambient_light_config["color"] = BLUE + + circle = self.circle + lighthouses = self.lighthouses + lights = self.lights + + circle.generate_target() + circle.target.scale_to_fit_width(2 * self.circle_radius) + circle.target.to_corner(DL) + self.circle = circle.target + + new_lighthouses = self.get_lighthouses() + new_lights = self.get_lights() + + self.clear() + self.play( + MoveToTarget(circle), + Transform(lighthouses, new_lighthouses), + Transform(lights, new_lights), + ApplyMethod( + self.observer_dot.move_to, + self.get_circle_point_at_proportion( + self.observer_fraction / self.num_lighthouses + ) + ), + MaintainPositionRelativeTo(self.observer, self.observer_dot), + ) + class Lemma1(DistanceProductScene): CONFIG = { "circle_radius": 2.5, "observer_fraction": 0.5, - # "ambient_light_config": { - # "num_levels": 5, - # "radius": 1, - # }, "lighthouse_height": 0.25, "lemma_text": "distance product = 2", } @@ -1468,14 +1892,14 @@ class PlugObserverIntoPolynomial(DistanceProductScene): i = polynomial[1].submobjects.index(eq) return polynomial[1][:i], polynomial[1][i], polynomial[1][i + 1:] - def get_lines(self): - dot = self.observer_dot - lines = VGroup(*[ - DashedLine(dot.get_center(), point) - for point in self.get_lh_points() - ]) - lines.set_stroke(width=2) - return lines + def get_lines(self, start_point=None): + return self.get_distance_lines( + start_point=start_point, + line_class=DashedLine + ) + + def get_observer_point(self, dummy_arg): + return self.observer_dot.get_center() class PlugObserverIntoPolynomial5Lighthouses(PlugObserverIntoPolynomial): @@ -1664,9 +2088,9 @@ class DistanceProductIsChordF(PlugObserverIntoPolynomial): self.add_plane() self.add_circle_group() self.add_polynomial("O") - self.add_observer_and_lines() + self.show_all_animations() - def add_observer_and_lines(self): + def show_all_animations(self): fraction = self.observer_fraction = 0.3 circle = self.circle @@ -1821,21 +2245,1218 @@ class DistanceProductIsChordF(PlugObserverIntoPolynomial): self.wait() - - - - - - - - - - - - - - - +class ProveLemma2(PlugObserverIntoPolynomial): + CONFIG = { + "include_lighthouses": False, + "num_lighthouses": 8, + # "ambient_light_config": CHEAP_AMBIENT_LIGHT_CONFIG, + # "add_lights_in_foreground": False, + } + + def construct(self): + self.add_plane() + self.add_circle_group() + self.add_polynomial("O") + + self.replace_first_lighthouse() + self.rearrange_polynomial() + self.plug_in_one() + + def replace_first_lighthouse(self): + light_to_remove = self.lights[0] + dot = self.observer_dot = Dot(color=self.observer_config["color"]) + dot.move_to(self.get_circle_point_at_proportion(0.5 / self.num_lighthouses)) + arrow = Vector(0.5 * DL, color=WHITE) + arrow.next_to(dot, UR, SMALL_BUFF) + O_label = self.O_dot_label = TexMobject("O") + O_label.match_color(dot) + O_label.add_background_rectangle() + O_label.next_to(arrow, UR, SMALL_BUFF) + + # First, move the lighthouse + self.add_foreground_mobject(dot) + self.play( + dot.move_to, light_to_remove, + MaintainPositionRelativeTo(arrow, dot), + MaintainPositionRelativeTo(O_label, dot), + path_arc=-TAU / 2 + ) + + black_rect = Rectangle( + height=6, width=3.5, + stroke_width=0, + fill_color=BLACK, + fill_opacity=1, + ) + black_rect.to_corner(DL, buff=0) + lines = self.get_lines(self.circle.get_right()) + labels = self.get_numeric_distance_labels() + column_group = self.get_distance_product_column( + black_rect.get_top() + MED_SMALL_BUFF * DOWN + ) + stacked_labels, h_line, times, product_decimal = column_group + q_marks = self.q_marks = TextMobject("???") + q_marks.move_to(product_decimal, LEFT) + q_marks.match_color(product_decimal) + + zero_rects = VGroup(*map(SurroundingRectangle, [dot, stacked_labels[0]])) + + self.play( + LaggedStart(ShowCreation, lines), + LaggedStart(FadeIn, labels), + ) + self.play( + FadeIn(black_rect), + ShowCreation(h_line), + Write(times), + ReplacementTransform(labels.copy(), stacked_labels) + ) + self.wait() + self.play(ReplacementTransform( + stacked_labels.copy(), + VGroup(product_decimal) + )) + self.wait() + self.add_foreground_mobject(zero_rects) + self.play(*map(ShowCreation, zero_rects)) + self.wait(2) + self.play( + VGroup(light_to_remove, zero_rects[0]).shift, FRAME_WIDTH * RIGHT / 2, + path_arc=-60 * DEGREES, + rate_func=running_start, + remover=True + ) + self.play( + VGroup(stacked_labels[0], zero_rects[1]).shift, 4 * LEFT, + rate_func=running_start, + remover=True, + ) + self.remove_foreground_mobjects(zero_rects) + self.play( + FadeOut(product_decimal), + FadeIn(q_marks) + ) + self.play(FadeOut(labels)) + self.wait() + + def rearrange_polynomial(self): + dot = self.observer_dot + lhs, equals, rhs = self.get_polynomial_split(self.polynomial) + polynomial_background = self.polynomial[0] + first_factor = rhs[:5] + remaining_factors = rhs[5:] + equals_remaining_factors = VGroup(equals, remaining_factors) + + # first_factor_rect = SurroundingRectangle(first_factor) + lhs_rect = SurroundingRectangle(lhs) + + frac_line = Line(LEFT, RIGHT, color=WHITE) + frac_line.match_width(lhs, stretch=True) + frac_line.next_to(lhs, DOWN, SMALL_BUFF) + O_minus_1 = TexMobject("\\left(", "O", "-", "1", "\\right)") + O_minus_1.next_to(frac_line, DOWN, SMALL_BUFF) + new_lhs_background = BackgroundRectangle(VGroup(lhs, O_minus_1), buff=SMALL_BUFF) + new_lhs_rect = SurroundingRectangle(VGroup(lhs, O_minus_1)) + + roots_of_unity_circle = VGroup(*[ + Circle(radius=0.2, color=YELLOW).move_to(point) + for point in self.get_lh_points() + ]) + for circle in roots_of_unity_circle: + circle.save_state() + circle.scale(4) + circle.fade(1) + + self.play(ShowCreation(lhs_rect)) + self.add_foreground_mobject(roots_of_unity_circle) + self.play(LaggedStart( + ApplyMethod, roots_of_unity_circle, + lambda m: (m.restore,) + )) + self.wait() + frac_line_copy = frac_line.copy() + self.play( + FadeIn(new_lhs_background), + polynomial_background.stretch, 0.8, 0, + polynomial_background.move_to, frac_line_copy, LEFT, + equals_remaining_factors.arrange_submobjects, RIGHT, SMALL_BUFF, + equals_remaining_factors.next_to, frac_line_copy, RIGHT, MED_SMALL_BUFF, + ReplacementTransform(first_factor, O_minus_1, path_arc=-90 * DEGREES), + ShowCreation(frac_line), + Animation(lhs), + ReplacementTransform(lhs_rect, new_lhs_rect), + ) + self.play( + roots_of_unity_circle[0].shift, FRAME_WIDTH * RIGHT / 2, + path_arc=(-60 * DEGREES), + rate_func=running_start, + remover=True + ) + + # Expand rhs + expanded_rhs = self.expanded_rhs = TexMobject( + "=", "1", "+", + "O", "+", + "O", "^2", "+", + "\\cdots", + "O", "^{N-1}" + ) + expanded_rhs.next_to(frac_line, RIGHT) + expanded_rhs.shift(LEFT) + expanded_rhs.scale(0.9) + expanded_rhs.set_color_by_tex("O", dot.get_color()) + + self.play( + polynomial_background.stretch, 1.8, 0, {"about_edge": LEFT}, + FadeIn(expanded_rhs), + equals_remaining_factors.scale, 0.9, + equals_remaining_factors.next_to, expanded_rhs, + VGroup( + new_lhs_background, lhs, frac_line, O_minus_1, + new_lhs_rect, + ).shift, LEFT, + ) + self.wait() + + def plug_in_one(self): + expanded_rhs = self.expanded_rhs + O_terms = expanded_rhs.get_parts_by_tex("O") + ones = VGroup(*[ + TexMobject("1").move_to(O_term, RIGHT) + for O_term in O_terms + ]) + ones.match_color(O_terms[0]) + + equals_1 = TexMobject("= 1") + equals_1.next_to(self.O_dot_label, RIGHT, SMALL_BUFF) + brace = Brace(expanded_rhs[1:], DOWN) + N_term = brace.get_text("N") + + product = DecimalNumber( + self.num_lighthouses, + num_decimal_points=3, + show_ellipsis=True + ) + product.move_to(self.q_marks, LEFT) + + self.play(Write(equals_1)) + self.play( + FocusOn(brace), + GrowFromCenter(brace) + ) + self.wait(2) + self.play(ReplacementTransform(O_terms, ones)) + self.wait() + self.play(Write(N_term)) + self.play(FocusOn(product)) + self.play( + FadeOut(self.q_marks), + FadeIn(product) + ) + self.wait() + + +class ArmedWithTwoKeyFacts(TeacherStudentsScene, DistanceProductScene): + CONFIG = { + "num_lighthouses": 6, + "ambient_light_config": { + "opacity_function": inverse_power_law(1, 1, 1, 6), + "radius": 1, + "num_levels": 100, + "max_opacity": 1, + }, + } + + def setup(self): + TeacherStudentsScene.setup(self) + DistanceProductScene.setup(self) + + def construct(self): + circle1 = self.circle + circle1.scale_to_fit_height(1.5) + circle1.to_corner(UL) + circle2 = circle1.copy() + circle2.next_to(circle1, DOWN, MED_LARGE_BUFF) + + wallis_product = get_wallis_product(n_terms=8) + + N = self.num_lighthouses + labels = VGroup() + for circle, f, dp in (circle1, 0.5, "2"), (circle2, 0, "N"): + self.circle = circle + lights = self.get_lights() + if f == 0: + lights.submobjects.pop(0) + observer = Dot(color=MAROON_B) + frac = f / N + point = self.get_circle_point_at_proportion(frac) + observer.move_to(point) + lines = self.get_distance_lines(point, line_class=DashedLine) + + label = TextMobject("Distance product = %s" % dp) + label.scale(0.7) + label.next_to(circle, RIGHT) + labels.add(label) + + group = VGroup(lines, observer, label) + self.play( + FadeIn(circle), + LaggedStart(FadeIn, VGroup(*it.chain(lights))), + LaggedStart( + FadeIn, VGroup(*it.chain(group.family_members_with_points())) + ), + self.teacher.change, "raise_right_hand", + self.get_student_changes(*["pondering"] * 3) + ) + wallis_product.move_to(labels).to_edge(RIGHT) + self.play( + LaggedStart(FadeIn, wallis_product), + self.teacher.change_mode, "hooray", + self.get_student_changes(*["thinking"] * 3, look_at_arg=wallis_product) + ) + self.wait(2) + + +class KeeperAndSailor(DistanceProductScene, PiCreatureScene): + CONFIG = { + "num_lighthouses": 9, + "circle_radius": 2.75, + # "ambient_light_config": CHEAP_AMBIENT_LIGHT_CONFIG, + "add_lights_in_foreground": False, # Keep this way + "text_scale_val": 0.7, + "observer_fraction": 0.5, + "keeper_color": BLUE, + "sailor_color": YELLOW_D, + "include_distance_labels_background_rectangle": False, + } + + def setup(self): + DistanceProductScene.setup(self) + PiCreatureScene.setup(self) + self.remove(*self.pi_creatures) + + def construct(self): + self.place_lighthouses() + self.introduce_observers() + self.write_distance_product_fraction() + self.break_down_distance_product_by_parts() + self.grow_circle_and_N() + self.show_limit_for_each_fraction() + self.show_limit_of_lhs() + + def place_lighthouses(self): + circle = self.circle + circle.to_corner(DL) + circle.shift(MED_SMALL_BUFF * UR) + circle.set_color(RED) + + lighthouses = self.get_lighthouses() + lights = self.get_lights() + for light in lights: + dot = Dot(radius=0.06).move_to(light) + dot.match_color(light) + light.add_to_back(dot) + origin = circle.get_center() + arrows = VGroup(*[ + Arrow(0.6 * (p - origin), 0.9 * (p - origin), buff=0).shift(origin) + for p in self.get_lh_points() + ]) + arrows.set_color(WHITE) + + words = TextMobject("N evenly-spaced \\\\ lighthouses") + words.scale(0.8) + words.move_to(origin) + + self.add(circle) + if self.add_lights_in_foreground: + self.add_foreground_mobject(lights) + self.add_foreground_mobject(words) + self.play( + LaggedStart(FadeIn, VGroup(*it.chain(lights))), + LaggedStart(FadeIn, lighthouses), + LaggedStart(GrowArrow, arrows), + ) + self.remove_foreground_mobjects(words) + self.play(FadeOut(words), FadeOut(arrows)) + self.wait() + + def introduce_observers(self): + keeper, sailor = observers = self.observers + keeper.target_point = self.get_keeper_point() + sailor.target_point = self.get_sailor_point() + + for pi, text in (keeper, "Keeper"), (sailor, "Sailor"): + pi.title = TextMobject(text) + pi.title.next_to(pi, UP) + pi.dot = Dot() + pi.dot.match_color(pi) + pi.dot.next_to(pi, LEFT) + pi.dot.set_fill(opacity=0) + + self.play(LaggedStart( + Succession, observers, + lambda m: (FadeIn, m, ApplyMethod, m.change, "wave_1") + )) + for pi in observers: + self.play( + FadeIn(pi.title), + pi.change, "plain" + ) + self.wait() + if self.add_lights_in_foreground: + self.add_foreground_mobjects(keeper, keeper.dot, keeper.title) + for pi in observers: + self.play( + pi.scale, 0.25, + pi.next_to, pi.target_point, RIGHT, SMALL_BUFF, + pi.dot.move_to, pi.target_point, + pi.dot.set_fill, {"opacity": 1}, + pi.title.scale, self.text_scale_val, + pi.title.next_to, pi.target_point, RIGHT, {"buff": 0.6}, + ) + if pi is sailor: + arcs = self.get_halfway_indication_arcs() + self.play(*map(ShowCreationThenDestruction, arcs)) + self.wait() + + def write_distance_product_fraction(self): + fraction = TexMobject( + "{\\text{Keeper's distance product}", "\\over", + "\\text{Sailor's distance product}}" + ) + fraction.scale(self.text_scale_val) + fraction.to_corner(UR) + + keeper_lines = self.get_distance_lines( + self.get_keeper_point(), + line_class=DashedLine + ) + sailor_lines = self.get_distance_lines( + self.get_sailor_point(), + line_class=DashedLine + ) + sailor_line_lengths = self.get_numeric_distance_labels(sailor_lines) + keeper_line_lengths = self.get_numeric_distance_labels(keeper_lines) + sailor_dp_column, keeper_dp_column = [ + self.get_distance_product_column( + 4 * RIGHT + 1.5 * UP, labels, frac + ) + for labels, frac in [ + (sailor_line_lengths, 0.5), + (keeper_line_lengths, 0), + ] + ] + sailor_dp_decimal = sailor_dp_column[-1] + sailor_dp_decimal_rect = SurroundingRectangle(sailor_dp_decimal) + keeper_dp_decimal = keeper_dp_column[-1] + keeper_dp_decimal_rect = SurroundingRectangle(keeper_dp_decimal) + keeper_top_zero_rect = SurroundingRectangle(keeper_dp_column[0][0]) + + # stacked_labels, h_line, times, product_decimal = column + + # Define result fraction + equals = self.distance_product_equals = TexMobject("=") + result_fraction = self.result_fraction = TexMobject( + "{N", "{\\text{distance} \\choose \\text{between obs.}}", "\\over", "2}" + ) + N, dist, frac_line, two = result_fraction + result_fraction.to_corner(UR) + equals.next_to(frac_line, LEFT) + for part in result_fraction: + part.save_state() + part.generate_target() + div = TexMobject("/") + first_denom = VGroup(two.target, div, dist) + first_denom.arrange_submobjects(RIGHT, buff=SMALL_BUFF) + first_denom.move_to(two, UP) + N.next_to(frac_line, UP, SMALL_BUFF) + + # Define terms to be removed + first_light_group = VGroup(self.lights[0], self.lighthouses[0]) + keeper_top_zero_group = VGroup(keeper_dp_column[0][0], keeper_top_zero_rect) + + new_keeper_dp_decimal = DecimalNumber( + self.num_lighthouses, + num_decimal_points=3, + ) + new_keeper_dp_decimal.replace(keeper_dp_decimal, dim_to_match=1) + new_keeper_dp_decimal.set_color(YELLOW) + + self.play(*map(ShowCreation, keeper_lines)) + self.play(ReplacementTransform( + keeper_lines.copy(), VGroup(fraction[0]) + )) + self.play(FadeOut(keeper_lines)) + self.play(*map(ShowCreation, sailor_lines)) + self.play( + ReplacementTransform( + sailor_lines.copy(), + VGroup(fraction[2]) + ), + ShowCreation(fraction[1]) + ) + self.wait() + self.play(LaggedStart(FadeIn, sailor_line_lengths)) + self.play(ReplacementTransform( + sailor_line_lengths.copy(), sailor_dp_column[0] + )) + self.play(FadeIn(sailor_dp_column[1:])) + self.play(ShowCreation(sailor_dp_decimal_rect)) + self.play( + fraction.next_to, equals, LEFT, + FadeIn(equals), + ShowCreation(frac_line), + ReplacementTransform(sailor_dp_decimal.copy(), two), + FadeOut(sailor_dp_decimal_rect) + ) + self.wait() + + # Note, sailor_lines and sailor_line_lengths get changed here + self.remove(*list(sailor_lines) + list(sailor_line_lengths)) + self.play( + FadeOut(sailor_dp_column), + ReplacementTransform(sailor_lines.deepcopy(), keeper_lines), + ReplacementTransform(sailor_line_lengths.deepcopy(), keeper_line_lengths), + ) + self.play(ReplacementTransform( + keeper_line_lengths.copy(), keeper_dp_column[0] + )) + self.play(FadeIn(keeper_dp_column[1:])) + self.wait() + self.play( + ShowCreation(keeper_dp_decimal_rect), + ShowCreation(keeper_top_zero_rect) + ) + self.wait(2) + + # Remove first lighthouse + self.play( + first_light_group.shift, 0.6 * FRAME_WIDTH * RIGHT, + keeper_top_zero_group.shift, 0.4 * FRAME_WIDTH * RIGHT, + FadeOut(keeper_dp_decimal), + FadeOut(keeper_dp_decimal_rect), + path_arc=-30 * DEGREES, + rate_func=running_start, + ) + self.remove(first_light_group, keeper_top_zero_group) + self.wait() + self.play(ReplacementTransform( + keeper_dp_column[0][1:].copy(), + VGroup(new_keeper_dp_decimal), + )) + self.wait() + self.play(ReplacementTransform(new_keeper_dp_decimal.copy(), N,)) + self.wait(2) + + sailor_lines[0].set_color(RED) + sailor_line_lengths[0].set_color(RED) + sailor_line_lengths[0].set_stroke(RED, 1) + self.remove(*list(keeper_lines) + list(keeper_line_lengths)) + self.play( + ReplacementTransform(keeper_lines.copy(), sailor_lines), + ReplacementTransform(keeper_line_lengths.copy(), sailor_line_lengths), + FadeOut(keeper_dp_column[:-1]), + FadeOut(new_keeper_dp_decimal), + ) + self.play( + Rotate(sailor_line_lengths[0], 30 * DEGREES, rate_func=wiggle) + ) + self.wait() + self.play( + ReplacementTransform(sailor_lines[0].copy(), dist), + FadeIn(div), + MoveToTarget(two), + ) + self.wait() + self.play( + two.restore, + FadeOut(div), + dist.restore, + N.restore, + ) + self.play( + FadeOut(sailor_lines), + FadeOut(sailor_line_lengths), + ) + self.wait() + + def break_down_distance_product_by_parts(self): + result_fraction = self.result_fraction + result_fraction_rect = SurroundingRectangle(result_fraction) + + product_parts = self.product_parts = TexMobject( + "{|L_1 - K|", "\\over", "|L_1 - S|}", "\\cdot", + "{|L_2 - K|", "\\over", "|L_2 - S|}", "\\cdot", + "{|L_3 - K|", "\\over", "|L_3 - S|}", "\\cdots", + ) + product_parts.set_color_by_tex_to_color_map({ + "K": BLUE, + "S": YELLOW, + }) + product_parts.scale_to_fit_width(0.4 * FRAME_WIDTH) + product_parts.next_to(result_fraction, DOWN, LARGE_BUFF, RIGHT) + product_parts.shift(MED_SMALL_BUFF * RIGHT) + + lighthouse_labels = self.get_light_labels() + self.lighthouse_labels = lighthouse_labels + + sailor_lines = self.get_sailor_lines() + sailor_lines.save_state() + keeper_lines = self.get_keeper_lines() + keeper_lines.save_state() + + sailor_length_braces = VGroup(VMobject()) # Add fluff first object + keeper_length_braces = VGroup(VMobject()) # Add fluff first object + triplets = [ + ("S", sailor_length_braces, DOWN), + ("K", keeper_length_braces, UP), + ] + for char, brace_group, vect in triplets: + for part in product_parts.get_parts_by_tex(char): + brace = Brace(part, vect, buff=SMALL_BUFF) + brace.match_color(part) + brace_group.add(brace) + + # Animations + self.remove(self.lights[0], self.lighthouses[0]) + if self.add_lights_in_foreground: + self.add_foreground_mobjects(lighthouse_labels[1:]) + self.play( + FadeOut(self.lighthouses[1:]), + FadeIn(lighthouse_labels[1:]), + ) + self.play( + LaggedStart(FadeIn, product_parts), + LaggedStart(FadeIn, sailor_lines, rate_func=there_and_back, remover=True), + LaggedStart(FadeIn, keeper_lines, rate_func=there_and_back, remover=True), + ) + sailor_lines.restore() + keeper_lines.restore() + self.wait() + + keeper_line = self.keeper_line = keeper_lines[1].copy() + sailor_line = self.sailor_line = sailor_lines[1].copy() + keeper_brace = keeper_length_braces[1].copy() + sailor_brace = sailor_length_braces[1].copy() + self.play( + ShowCreation(keeper_line), + GrowFromCenter(keeper_brace), + ) + self.wait() + self.play( + ShowCreation(sailor_line), + GrowFromCenter(sailor_brace), + ) + self.wait() + for i in range(2, 4): + self.play( + Transform(keeper_line, keeper_lines[i]), + Transform(keeper_brace, keeper_length_braces[i]), + ) + self.play( + Transform(sailor_line, sailor_lines[i]), + Transform(sailor_brace, sailor_length_braces[i]), + ) + self.wait() + for i in range(4, self.num_lighthouses): + anims = [ + Transform(keeper_line, keeper_lines[i]), + Transform(sailor_line, sailor_lines[i]), + ] + if i == 4: + anims += [ + FadeOut(sailor_brace), + FadeOut(keeper_brace), + ] + self.play(*anims) + self.play(FocusOn(result_fraction)) + self.play(ShowPassingFlash(result_fraction_rect)) + self.wait(3) + + def grow_circle_and_N(self, circle_scale_factor=2, N_multiple=3): + circle = self.circle + lights = self.lights + labels = self.lighthouse_labels + keeper_line = self.keeper_line + sailor_line = self.sailor_line + keeper = self.keeper + sailor = self.sailor + half_N = self.num_lighthouses / 2 + + circle.generate_target() + for pi in keeper, sailor: + for mob in pi, pi.dot, pi.title: + mob.generate_target() + + circle.target.scale(circle_scale_factor) + circle.target.move_to(FRAME_WIDTH * LEFT / 2 + SMALL_BUFF * RIGHT) + self.circle = circle.target + self.num_lighthouses = int(N_multiple * self.num_lighthouses) + new_lights = self.get_lights() + for light in new_lights: + light.scale(1.0 / circle_scale_factor) + new_labels = self.get_light_labels() + self.keeper_lines = self.get_keeper_lines() + self.sailor_lines = self.get_sailor_lines() + + for group in lights, labels, new_lights, new_labels: + group[0].fade(1) + + keeper.dot.target.move_to(self.get_keeper_point()) + sailor.dot.target.move_to(self.get_sailor_point()) + for pi in keeper, sailor: + pi.target.scale(0) + pi.target.move_to(pi.dot.target) + pi.title.target.scale(0.85) + pi.title.target.next_to(pi.dot.target, RIGHT, SMALL_BUFF) + + self.circle = circle + + for mob in lights, labels: + for x in range(len(new_lights) - len(mob)): + mob.submobjects.insert(half_N + 1, VectorizedPoint(circle.get_left())) + + light_anim = ReplacementTransform(lights, new_lights) + self.play( + MoveToTarget(circle), + Transform(keeper_line, self.keeper_lines[-1]), + Transform(sailor_line, self.sailor_lines[-1]), + ReplacementTransform(labels, new_labels), + light_anim, + *[ + MoveToTarget(part) + for pi in self.observers + for part in pi, pi.dot, pi.title + ], + run_time=2 + ) + if self.add_lights_in_foreground: + self.remove_foreground_mobjects(*self.lights) + self.remove_foreground_mobjects(*self.lighthouse_labels) + self.add_foreground_mobjects(new_lights, new_labels) + self.wait() + self.lights = new_lights + self.lighthouse_labels = new_labels + + def show_limit_for_each_fraction(self): + product_parts = self.product_parts + keeper_line = self.keeper_line + keeper_lines = self.keeper_lines + sailor_line = self.sailor_line + sailor_lines = self.sailor_lines + labels = self.lighthouse_labels + + center = self.circle.get_center() + center_dot = Dot(center) + lh_points = self.get_lh_points() + sailor_point = self.get_sailor_point() + keeper_point = self.get_keeper_point() + + def get_angle_mob(p1, p2): + angle1 = angle_of_vector(p1 - center) + angle2 = angle_of_vector(p2 - center) + arc = Arc(start_angle=angle1, angle=(angle2 - angle1), radius=1) + arc.shift(center) + return VGroup( + center_dot, + Line(center, p1), + Line(center, p2), + arc, + ) + + angle_mob = get_angle_mob(lh_points[1], keeper_point) + + ratios = VGroup(*[ + product_parts[i:i + 3] + for i in [0, 4, 8] + ]) + term_rects = self.get_term_rects(ratios) + + limit_fractions = VGroup( + TexMobject("{2", "\\over", "1}"), + TexMobject("{4", "\\over", "3}"), + TexMobject("{6", "\\over", "5}"), + ) + limit_arrows = VGroup() + for rect, fraction in zip(term_rects, limit_fractions): + fraction.next_to(rect, DOWN, LARGE_BUFF) + arrow = Arrow(rect, fraction, color=WHITE) + limit_arrows.add(arrow) + + approx = TexMobject("\\approx") + approx.scale(1.5) + approx.rotate(90 * DEGREES) + approx.move_to(limit_arrows[0]) + + braces = self.get_all_circle_braces() + + # Show first lighthouse + term_rect = term_rects[0].copy() + self.play( + Transform(keeper_line, keeper_lines[1]), + Transform(sailor_line, sailor_lines[1]), + FadeIn(term_rect), + path_arc=-180 * DEGREES + ) + self.wait(2) + self.play( + FadeOut(VGroup(keeper_line, sailor_line)), + FadeIn(braces[:2]), + FadeIn(angle_mob) + ) + self.wait() + self.play(Transform(angle_mob, get_angle_mob(lh_points[1], sailor_point))) + self.wait(2) + self.play( + Write(approx), + ReplacementTransform(ratios[0].copy(), limit_fractions[0]), + FadeOut(angle_mob) + ) + self.wait() + self.play(ReplacementTransform(approx, limit_arrows[0])) + self.let_N_approach_infinity(braces[:2]) + + # Show second lighthouse + self.play( + Transform(term_rect, term_rects[1]), + ReplacementTransform(limit_arrows[0].copy(), limit_arrows[1]), + FadeIn(braces[2:4]) + ) + for group, color in (braces[:4], self.keeper_color), (braces[1:4], self.sailor_color): + self.play( + group.scale, 0.95, {"about_point": center}, + group.set_color, color, + rate_func=there_and_back + ) + self.wait(0.5) + self.play( + ReplacementTransform(ratios[1].copy(), limit_fractions[1]) + ) + self.wait() + + # Show third lighthouse + braces[4:6].set_color(YELLOW) + self.play( + Transform(term_rect, term_rects[2]), + ReplacementTransform(limit_arrows[1].copy(), limit_arrows[2]), + FadeIn(braces[4:6]), + braces[1:4].set_color, YELLOW, + ReplacementTransform(limit_fractions[1].copy(), limit_fractions[2]) + ) + self.let_N_approach_infinity(braces[:6]) + self.wait() + + # Set up for lighthouse "before" keeper + ccw_product_group = VGroup(product_parts, limit_arrows, limit_fractions) + cw_product_parts = TexMobject( + "\\cdots", "{|L_{-3} - K|", "\\over", "|L_{-3} - S|}", + "\\cdot", "{|L_{-2} - K|", "\\over", "|L_{-2} - S|}", + "\\cdot", "{|L_{-1} - K|", "\\over", "|L_{-1} - S|}", + ) + cw_product_parts.match_height(product_parts) + cw_product_parts.set_color_by_tex_to_color_map({ + "K": BLUE, + "S": YELLOW, + }) + cw_product_parts.move_to(ratios, RIGHT) + cw_ratios = VGroup(*[cw_product_parts[i:i + 3] for i in 9, 5, 1]) + cw_term_rects = self.get_term_rects(cw_ratios) + cw_limit_fractions = VGroup( + TexMobject("{2", "\\over", "3}"), + TexMobject("{4", "\\over", "5}"), + TexMobject("{6", "\\over", "7}"), + ) + cw_limit_arrows = VGroup() + for rect, fraction in zip(cw_term_rects, cw_limit_fractions): + fraction.next_to(rect, DOWN, LARGE_BUFF) + arrow = Arrow(rect, fraction, color=WHITE) + cw_limit_arrows.add(arrow) + + cw_product_parts.save_state() + cw_product_parts.next_to(product_parts, RIGHT, LARGE_BUFF) + + cw_label_rects = self.get_term_rects(labels[-1:-5:-1]) + cw_label_rects.set_color(RED) + + braces[-8:].set_color(BLUE) + braces[0].set_color(YELLOW) + + def show_braces(n): + cw_group = braces[-2 * n:] + for group in cw_group, VGroup(braces[0], *cw_group): + self.play( + group.scale, 0.95, {"about_point": center}, + rate_func=there_and_back + ) + self.wait(0.5) + + # Animated clockwise-from-keeper terms + self.play( + ccw_product_group.scale, 0.5, {"about_edge": UL}, + ccw_product_group.to_corner, UL, + FadeOut(term_rect), + FadeOut(braces[:6]), + cw_product_parts.restore, + ) + term_rect = cw_term_rects[0].copy() + self.play(LaggedStart(ShowCreationThenDestruction, cw_label_rects)) + self.wait() + self.play( + FadeIn(term_rect), + FadeIn(braces[-2:]), + FadeIn(braces[0]), + ) + show_braces(1) + self.play( + GrowArrow(cw_limit_arrows[0]), + FadeIn(cw_limit_fractions[0]) + ) + self.wait() + + # Second and third lighthouse before + self.play( + Transform(term_rect, cw_term_rects[1]), + ReplacementTransform(cw_limit_arrows[0].copy(), cw_limit_arrows[1]), + FadeIn(braces[-4:-2]), + Write(cw_limit_fractions[1]) + ) + show_braces(2) + self.wait() + self.play( + Transform(term_rect, cw_term_rects[2]), + ReplacementTransform(cw_limit_arrows[1].copy(), cw_limit_arrows[2]), + FadeIn(braces[-6:-4]), + Write(cw_limit_fractions[2]) + ) + show_braces(3) + self.let_N_approach_infinity(VGroup(braces[0], *braces[-6:])) + self.wait() + + # Organize fractions + fractions = VGroup(*it.chain(*zip( + limit_fractions, cw_limit_fractions, + ))) + fractions.generate_target() + wallis_product = VGroup() + dots = VGroup() + for fraction in fractions.target: + fraction.match_height(cw_limit_fractions[0]) + wallis_product.add(fraction) + dot = TexMobject("\\cdot") + wallis_product.add(dot) + dots.add(dot) + final_dot = TexMobject("\\cdots") + for group in wallis_product, dots: + group.submobjects[-1] = final_dot + wallis_product.arrange_submobjects(RIGHT, buff=MED_SMALL_BUFF) + wallis_product.to_edge(RIGHT) + + self.play( + FadeOut(limit_arrows), + FadeOut(cw_limit_arrows), + FadeOut(braces[-6:]), + FadeOut(braces[0]), + FadeOut(term_rect), + ) + self.play( + cw_product_parts.scale, 0.5, + cw_product_parts.next_to, product_parts, DOWN, {"aligned_edge": LEFT}, + MoveToTarget(fractions), + Write(dots), + run_time=2, + path_arc=90 * DEGREES + ) + self.wait() + + self.wallis_product = VGroup(dots, fractions) + self.observers_brace = braces[0] + + def show_limit_of_lhs(self): + brace = self.observers_brace + wallis_product = self.wallis_product + result_fraction = self.result_fraction + N, dist, over, two = result_fraction + distance_product_equals = self.distance_product_equals + + result_rect = SurroundingRectangle(result_fraction) + result_rect.set_color(WHITE) + + equals = TexMobject("=") + equals.next_to(brace, LEFT, SMALL_BUFF) + approx1, approx2, approx3 = [TexMobject("\\approx") for x in range(3)] + approx1.next_to(brace, LEFT, SMALL_BUFF) + half_two_pi_over_N = TexMobject( + "{1", "\\over", "2}", "{2", "\\pi", "\\over", "N}", + ) + pi = half_two_pi_over_N.get_part_by_tex("\\pi") + half_two_pi_over_N.next_to(approx1, LEFT) + approx2.next_to(half_two_pi_over_N, LEFT, SMALL_BUFF) + + approx3.move_to(distance_product_equals) + + pi_over_N = TexMobject("(", "\\pi", "/", "N", ")") + pi_over_N.next_to(N, RIGHT) + N_shift = MED_LARGE_BUFF * RIGHT + pi_over_N.shift(N_shift) + + pi_halves = TexMobject("{\\pi", "\\over", "2}") + pi_halves.next_to(result_rect, DOWN, LARGE_BUFF) + pi_halves.shift(RIGHT) + pi_halves_arrow = Arrow( + result_rect.get_bottom(), + pi_halves.get_top(), + color=WHITE, + buff=SMALL_BUFF + ) + + last_equals = TexMobject("=") + last_equals.next_to(pi_halves, LEFT) + + self.play(ShowCreation(result_rect)) + self.wait() + self.play( + dist.next_to, equals, LEFT, + FadeIn(equals), + GrowFromCenter(brace), + ) + self.wait() + approx2.next_to(dist, LEFT, SMALL_BUFF) + half_two_pi_over_N.next_to(approx2, LEFT) + self.play( + Write(half_two_pi_over_N), + FadeIn(approx2) + ) + self.wait() + self.play( + FadeOut(half_two_pi_over_N[:4]), + pi.shift, SMALL_BUFF * LEFT, + ) + self.wait() + self.play( + ReplacementTransform( + half_two_pi_over_N[-3:].copy(), + pi_over_N[1:4] + ), + FadeIn(pi_over_N[0]), + FadeIn(pi_over_N[-1]), + N.shift, N_shift * RIGHT, + ReplacementTransform(distance_product_equals, approx3) + ) + self.wait() + self.play( + GrowArrow(pi_halves_arrow), + wallis_product.shift, DOWN, + ) + self.play(Write(pi_halves)) + self.wait(2) + self.play( + wallis_product.next_to, last_equals, LEFT, 2 * SMALL_BUFF, + FadeIn(last_equals) + ) + final_rect = SurroundingRectangle( + VGroup(wallis_product, pi_halves), + buff=MED_SMALL_BUFF + ) + final_rect.set_color(YELLOW) + self.play(ShowCreation(final_rect)) + self.wait(2) + + # + + def let_N_approach_infinity(self, braces=None, factor=4, run_time=5, zoom_in_after=False): + lights = self.lights + labels = self.lighthouse_labels + keeper, sailor = self.observers + circle = self.circle + + if braces is None: + braces = VGroup() + + start_fraction = 1.0 / self.num_lighthouses + target_fraction = start_fraction / factor + half_N = self.num_lighthouses / 2 + + fraction_tracker = ValueTracker(start_fraction) + + def get_fraction(): + return fraction_tracker.get_value() + + def get_ks_distance(): + return np.linalg.norm(keeper.dot.get_center() - sailor.dot.get_center()) + + def update_title_heights(*titles): + for title in titles: + if not hasattr(title, "original_height"): + title.original_height = title.get_height() + title.scale_to_fit_height(min( + title.original_height, + 0.8 * get_ks_distance(), + )) + if len(titles) > 1: + return titles + else: + return titles[0] + + initial_light_width = lights[0].get_width() + + def update_lights(lights): + for k in range(-half_N, half_N + 1): + if k == 0: + continue + light = lights[k] + light = light.scale_to_fit_width( + (get_fraction() / start_fraction) * initial_light_width + ) + point = self.get_circle_point_at_proportion(k * get_fraction()) + light.move_source_to(point) + return lights + + def update_braces(braces): + for brace in braces: + f1 = brace.fraction1 * (get_fraction() / start_fraction) + f2 = brace.fraction2 * (get_fraction() / start_fraction) + new_brace = self.get_circle_brace(f1, f2) + new_brace.match_style(brace) + Transform(brace, new_brace).update(1) + return braces + + light_update_anim = UpdateFromFunc(lights, update_lights) + label_update_anim = UpdateFromFunc( + labels, + lambda ls: self.position_labels_outside_lights(update_title_heights(*ls)), + ) + sailor_dot_anim = UpdateFromFunc( + sailor.dot, + lambda d: d.move_to(self.get_circle_point_at_proportion(get_fraction() / 2)) + ) + sailor_title_anim = UpdateFromFunc( + sailor.title, + lambda m: update_title_heights(m).next_to(sailor.dot, RIGHT, SMALL_BUFF) + ) + keeper_title_anim = UpdateFromFunc( + keeper.title, + lambda m: update_title_heights(m).next_to(keeper.dot, RIGHT, SMALL_BUFF) + ) + braces_update_anim = UpdateFromFunc(braces, update_braces) + + lights[0].fade(1) + labels[0].fade(1) + + all_updates = [ + light_update_anim, + label_update_anim, + sailor_dot_anim, + sailor_title_anim, + keeper_title_anim, + braces_update_anim, + ] + + self.play( + fraction_tracker.set_value, target_fraction, + *all_updates, + run_time=run_time + ) + if zoom_in_after: + self.play( + circle.scale, factor, {"about_point": circle.get_right()}, + *all_updates, + run_time=1 + ) + self.wait() + self.play( + circle.scale, 1.0 / factor, {"about_point": circle.get_right()}, + *all_updates, + run_time=1 + ) + self.wait() + self.play( + fraction_tracker.set_value, start_fraction, + *all_updates, + run_time=run_time / 2 + ) + + def get_keeper_point(self): + return self.get_circle_point_at_proportion(0) + + def get_sailor_point(self): + return self.get_circle_point_at_proportion(0.5 / self.num_lighthouses) + + def create_pi_creatures(self): + keeper = self.keeper = PiCreature(color=self.keeper_color).flip() + sailor = self.sailor = PiCreature(color=self.sailor_color).flip() + observers = self.observers = VGroup(keeper, sailor) + observers.scale(0.5) + keeper.shift(4 * RIGHT + 2 * DOWN) + sailor.shift(4 * RIGHT + 2 * UP) + return VGroup(keeper, sailor) + + def get_light_labels(self): + labels = VGroup() + for count, point in enumerate(self.get_lh_points()): + if count > self.num_lighthouses / 2: + count -= self.num_lighthouses + label = TexMobject("L_{%d}" % count) + label.scale(0.8) + labels.add(label) + self.position_labels_outside_lights(labels) + return labels + + def position_labels_outside_lights(self, labels): + center = self.circle.get_center() + for light, label in zip(self.lights, labels): + point = light[0].get_center() + vect = (point - center) + norm = np.linalg.norm(vect) + buff = label.get_height() + vect *= (norm + buff) / norm + label.move_to(center + vect) + return labels + + def get_keeper_lines(self, line_class=Line): + lines = self.get_distance_lines(self.get_keeper_point()) + lines.set_stroke(self.keeper_color, 3) + return lines + + def get_sailor_lines(self, line_class=Line): + lines = self.get_distance_lines(self.get_sailor_point()) + lines.set_stroke(self.sailor_color, 3) + return lines + + def get_term_rects(self, terms): + return VGroup(*[ + SurroundingRectangle(term, color=WHITE) + for term in terms + ]) + + def get_circle_brace(self, f1, f2): + line = Line( + self.get_circle_point_at_proportion(f1), + self.get_circle_point_at_proportion(f2), + ) + angle = (line.get_angle() + TAU / 2) % TAU + scale_factor = 1.5 + line.rotate(-angle, about_point=ORIGIN) + line.scale(scale_factor, about_point=ORIGIN) + brace = Brace(line, DOWN, buff=SMALL_BUFF) + group = VGroup(line, brace) + group.scale(1.0 / scale_factor, about_point=ORIGIN) + group.rotate(angle, about_point=ORIGIN) + + # Keep track of a fraction between -0.5 and 0.5 + if f1 > 0.5: + f1 -= 1 + if f2 > 0.5: + f2 -= 1 + brace.fraction1 = f1 + brace.fraction2 = f2 + return brace + + def get_all_circle_braces(self): + fractions = np.linspace(0, 1, 2 * self.num_lighthouses + 1) + return VGroup(*[ + self.get_circle_brace(f1, f2) + for f1, f2 in zip(fractions, fractions[1:]) + ]) diff --git a/for_3b1b_videos/pi_creature_scene.py b/for_3b1b_videos/pi_creature_scene.py index 3f9da5db..73d925f3 100644 --- a/for_3b1b_videos/pi_creature_scene.py +++ b/for_3b1b_videos/pi_creature_scene.py @@ -39,7 +39,7 @@ class PiCreatureScene(Scene): } def setup(self): - self.pi_creatures = self.create_pi_creatures() + self.pi_creatures = VGroup(*self.create_pi_creatures()) self.pi_creature = self.get_primary_pi_creature() if self.pi_creatures_start_on_screen: self.add(*self.pi_creatures) diff --git a/mobject/geometry.py b/mobject/geometry.py index f7c3e53c..478c079d 100644 --- a/mobject/geometry.py +++ b/mobject/geometry.py @@ -439,7 +439,13 @@ class DashedLine(Line): def generate_points(self): length = np.linalg.norm(self.end - self.start) + if length == 0: + self.add(Line(self.start, self.end)) + return self num_interp_points = int(length / self.dashed_segment_length) + # Even number ensures that start and end points are hit + if num_interp_points % 2 == 1: + num_interp_points += 1 points = [ interpolate(self.start, self.end, alpha) for alpha in np.linspace(0, 1, num_interp_points) diff --git a/mobject/mobject.py b/mobject/mobject.py index 00bc8502..123b5206 100644 --- a/mobject/mobject.py +++ b/mobject/mobject.py @@ -115,7 +115,7 @@ class Mobject(Container): def copy(self): # TODO, either justify reason for shallow copy, or # remove this redundancy everywhere - #return self.deepcopy() + # return self.deepcopy() copy_mobject = copy.copy(self) copy_mobject.points = np.array(self.points) diff --git a/mobject/shape_matchers.py b/mobject/shape_matchers.py index 7ecbb457..4e341e0d 100644 --- a/mobject/shape_matchers.py +++ b/mobject/shape_matchers.py @@ -2,6 +2,7 @@ from __future__ import absolute_import from constants import * +from mobject.types.vectorized_mobject import VMobject from mobject.geometry import Rectangle from mobject.geometry import Line from mobject.types.vectorized_mobject import VGroup @@ -39,8 +40,21 @@ class BackgroundRectangle(SurroundingRectangle): self.set_fill(opacity=b * self.original_fill_opacity) return self - def set_color(self): - # Can't be changin' me! + def set_style_data(self, + stroke_color=None, + stroke_width=None, + fill_color=None, + fill_opacity=None, + family=True + ): + # Unchangable style, except for fill_opacity + VMobject.set_style_data( + self, + stroke_color=BLACK, + stroke_width=0, + fill_color=BLACK, + fill_opacity=fill_opacity + ) return self def get_fill_color(self): diff --git a/mobject/svg/drawings.py b/mobject/svg/drawings.py index 6206c33c..e22ec529 100644 --- a/mobject/svg/drawings.py +++ b/mobject/svg/drawings.py @@ -226,6 +226,7 @@ class Laptop(VGroup): body.set_fill(self.shaded_body_color, opacity=1) body.sort_submobjects(lambda p: p[2]) body[-1].set_fill(self.body_color) + screen_plate = body.copy() keyboard = VGroup(*[ VGroup(*[ Square(**self.key_color_kwargs) @@ -243,7 +244,6 @@ class Laptop(VGroup): keyboard.shift(MED_SMALL_BUFF * UP) body.add(keyboard) - screen_plate = body.copy() screen_plate.stretch(self.screen_thickness / self.body_dimensions[2], dim=2) screen = Rectangle( diff --git a/mobject/svg/svg_mobject.py b/mobject/svg/svg_mobject.py index 3f405005..5c02191f 100644 --- a/mobject/svg/svg_mobject.py +++ b/mobject/svg/svg_mobject.py @@ -165,7 +165,7 @@ class SVGMobject(VMobject): # input preprocessing if fill_color in ["", "none", "#FFF", "#FFFFFF"] or Color(fill_color) == Color(WHITE): opacity = 0 - fill_color = BLACK # shdn't be necessary but avoids error msgs + fill_color = BLACK # shdn't be necessary but avoids error msgs if fill_color in ["#000", "#000000"]: fill_color = WHITE if stroke_color in ["", "none", "#FFF", "#FFFFFF"] or Color(stroke_color) == Color(WHITE): @@ -175,10 +175,6 @@ class SVGMobject(VMobject): stroke_color = WHITE if stroke_width in ["", "none", "0"]: stroke_width = 0 - - # is there sth to draw? - if opacity == 0 and stroke_width == 0: - return if corner_radius in ["", "0", "none"]: corner_radius = 0 @@ -187,22 +183,22 @@ class SVGMobject(VMobject): if corner_radius == 0: mob = Rectangle( - width = float(rect_element.getAttribute("width")), - height = float(rect_element.getAttribute("height")), - stroke_width = stroke_width, - stroke_color = stroke_color, - fill_color = fill_color, - fill_opacity = opacity + width=float(rect_element.getAttribute("width")), + height=float(rect_element.getAttribute("height")), + stroke_width=stroke_width, + stroke_color=stroke_color, + fill_color=fill_color, + fill_opacity=opacity ) else: mob = RoundedRectangle( - width = float(rect_element.getAttribute("width")), - height = float(rect_element.getAttribute("height")), - stroke_width = stroke_width, - stroke_color = stroke_color, - fill_color = fill_color, - fill_opacity = opacity, - corner_radius = corner_radius + width=float(rect_element.getAttribute("width")), + height=float(rect_element.getAttribute("height")), + stroke_width=stroke_width, + stroke_color=stroke_color, + fill_color=fill_color, + fill_opacity=opacity, + corner_radius=corner_radius ) mob.shift(mob.get_center() - mob.get_corner(UP + LEFT)) diff --git a/utils/bezier.py b/utils/bezier.py index 6097e130..c0926725 100644 --- a/utils/bezier.py +++ b/utils/bezier.py @@ -3,7 +3,7 @@ import numpy as np from scipy import linalg from utils.simple_functions import choose -CLOSED_THRESHOLD = 0.0 +CLOSED_THRESHOLD = 0.001 def bezier(points): @@ -98,7 +98,8 @@ def get_smooth_handle_points(points): def solve_func(b): return linalg.solve_banded((l, u), diag, b) - if is_closed(points): + use_closed_solve_function = is_closed(points) + if use_closed_solve_function: # Get equations to relate first and last points matrix = diag_to_matrix((l, u), diag) # last row handles second derivative @@ -109,11 +110,15 @@ def get_smooth_handle_points(points): b[0] = 2 * points[0] b[-1] = np.zeros(dim) - def solve_func(b): + def closed_curve_solve_func(b): return linalg.solve(matrix, b) + handle_pairs = np.zeros((2 * num_handles, dim)) for i in range(dim): - handle_pairs[:, i] = solve_func(b[:, i]) + if use_closed_solve_function: + handle_pairs[:, i] = closed_curve_solve_func(b[:, i]) + else: + handle_pairs[:, i] = solve_func(b[:, i]) return handle_pairs[0::2], handle_pairs[1::2]